Parabolic Equation Method Simulation Code for Calculating Long-Range Underwater Acoustic Transmission Loss

The Parabolic Equation Method (PEM) is a classical approach for calculating long-range underwater acoustic transmission loss, particularly suitable for long-distance sound field prediction and deep-sea acoustic propagation analysis. This method utilizes simplified wave equations to model acoustic wave propagation characteristics in complex marine environments. Code implementation typically involves solving the Helmholtz equation through parabolic approximation using finite difference or split-step Fourier algorithms.

The core concept of PEM employs the paraxial wave assumption, reducing the three-dimensional wave equation to a two-dimensional parabolic equation. Numerical solutions are implemented through step-by-step marching algorithms that calculate sound field distribution iteratively. The method offers high computational efficiency, making it suitable for large-scale marine acoustic propagation problems. Typical implementations use range-dependent depth grids with Crank-Nicolson or finite-difference schemes for stable numerical solutions.

In practical simulations, parameters such as water column stratification, seabed characteristics, and source frequency must be considered, as these significantly affect transmission loss calculations. The code implementation includes environmental parameter modules that handle sound speed profiles, bottom properties, and absorption coefficients. By adjusting boundary conditions and environmental parameters, the simulation can model sound field distributions under various marine conditions. Boundary handling typically involves impedance matching for seabed interactions and surface reflection coefficients.

Far-field transmission loss results are typically presented as transmission loss contour maps or two-dimensional field distribution plots, visually demonstrating acoustic energy attenuation patterns with respect to distance and depth. This method finds extensive applications in sonar performance evaluation, underwater communication system design, and marine environmental noise analysis. The output visualization often includes dB-scale color mapping and depth-range coordinate systems for professional analysis.